Double Core Evolution. VI. Effects of Gravitational Torques
Abstract
The influence of gravitaional torques during the late stages of common envelope evolution of a binary star system consisting of a 3 stellar mass red giant and a 1 stellar mass companion star is studied. The numerical results of two-dimensional hydrodynamical simulations of the binary in its orbital plane indicate that gravitational torques are important for distances of approximately 3 times the orbital separation of the binary system. It is shown, for the first time, that when the companion has spiraled to a radius of 3 x 1011 cm from the center of the red giant, matter in its immediate vicinity is brought into a state of corotation with the orbital motion. The degree of spin-up is a function of orbital phase with the departure from corotation increasing for matter which experienced the previous companion passage the earliest. A low-density region, consequently, is formed over a significant fraction of the orbit. This region is limited in its radical extent to a width approximately given by the size of the tidal lobe of the low-mass companion. Throughout the remainder of the common envelope, the matter rotates differentially. In particular, exterior to the low-density region, the specific angular momentum tends toward a spatially constant value. As a result of the gravitaional interaction, energy is found to be released from the binary orbit at a rate comparable to that obtained from a frictional drag calculation which employs the unmodified Bondi-Hoyle accretion radius. These rates are larger by a factor of a few in comparison with rates deduced from the use of a modified accretion radius which takes into account density gradients in the accretion flow. Termination of the spiral-in phase, as a result of spin-up of envelope material to the orbital velocity, is strongly indicated when the companion has reached a radius of approximately 3 x 1011 cm. This effect is facilitaed by the condition that a steep density gradient exists in the red giant companion near that radius. Thus, these two-dimensional nonaxisymmetric calulations strengthen the conclusions reached by previous axisymmetric calculations, which also indicated termination near the same radius, but for different physical reasons. This work also indicates that the common envelope phase ends with a slow material outflow; future three-dimensional studies will be required to confirm this conclusion.
- Publication:
-
The Astrophysical Journal
- Pub Date:
- August 1994
- DOI:
- 10.1086/174482
- Bibcode:
- 1994ApJ...431..247T
- Keywords:
-
- Binary Stars;
- Gravitational Effects;
- Stellar Envelopes;
- Stellar Evolution;
- Stellar Interiors;
- Stellar Mass;
- Angular Momentum;
- Computational Astrophysics;
- Hydrodynamics;
- Mass Transfer;
- Stellar Orbits;
- Torque;
- Astrophysics;
- HYDRODYNAMICS;
- STARS: BINARIES: CLOSE;
- STARS: EVOLUTION;
- STARS: INTERIORS